In the literature, are there some researchs on non commutative analogy of Leray-Hirsch theorem in the context of non commutative Principal bundles?
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2$\begingroup$ I haven't heard of a Leary Hirsch theorem, but there is something called the Leray-Hirsch theorem that talks about bundles. Is that what you are referencing? $\endgroup$– Ryan BudneyCommented Jun 2, 2019 at 16:39
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1$\begingroup$ @RyanBudney yes. I am sorry for my typos. I revise it. Thank you! $\endgroup$– Ali TaghaviCommented Jun 2, 2019 at 17:16
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1$\begingroup$ There are quantum versions of Leray-Hirsch on toric bundles, in the literature. Are you interested in smt like this? $\endgroup$– Konstantinos KanakoglouCommented Aug 16, 2019 at 16:59
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1$\begingroup$ @KonstantinosKanakoglou Thanks for informing me of this version! yes i am interested in this formulation. $\endgroup$– Ali TaghaviCommented Aug 16, 2019 at 19:01
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1 Answer
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First of all, let me make clear that by no means would i like to pretend any expertise on the topic (in fact i feel i have a limited understanding of AG in general). However, the question reminded me that i recently came across a "quantum" generalization of Leray-Hirsch theorem (while i was actually searching for something quite different).
So, maybe you would be interested to take a look at:
- Quantum Cohomology under Birational Maps and Transitions, arXiv:1705.04799 [math.AG]
and the references therein; especially:
Invariance of quantum rings under ordinary flops II: A quantum Leray–Hirsch theorem, Algebraic Geometry 3 (5) (2016) 615–653,
Invariance of quantum rings under ordinary flops III: A quantum splitting principle, Cambridge Journal of Mathematics, Volume 4, Number 3, 333–401, 2016
Hope that is of some interest for your purposes.
answered Aug 17, 2019 at 0:06
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1$\begingroup$ thanks very much, very great. I try to read the links you kindly provided in the answer $\endgroup$ Commented Aug 17, 2019 at 0:26